bus the north island nakedbus.com and citylink.co.nz are great and cheap
you probably have a good idea of what you want to see but I'll point out some musts anyway
-Don't waste anytime in auckland. if you fly in try to book a bus out that same day. should be easy enough. if I ever go back I will book a bus at the airport
-Definitely do the tongariro crossing.
-If you are with some cool people rent a campervan and drive around the coromandel peninsula and camp out where you can. It's really beautiful there. but If you are alone that area might be a little boring.
-hot water beach is pretty neat
south island:
rent a camper van for the south island
-franz josef is a must
-make sure you see lake hawae and lake wanaka in the day light on the way to queenstown. it really is something special. just stunning scenery
-swim with the dolphins or seals in kaikoura. I missed out but my friends all raved about it. they said they were in the water with at least 500 dolphins and that the seals were like big puppies